Reed-Solomon Turbo Product Codes for Optical Communications: From Code Optimization to Decoder Design

Turbo product codes (TPCs) are an attractive solution to improve link budgets and reduce systems costs by relaxing the requirements on expensive optical devices in high capacity optical transport systems. In this paper, we investigate the use of Reed-Solomon (RS) turbo product codes for 40 Gbps transmission over optical transport networks and 10 Gbps transmission over passive optical networks. An algorithmic study is first performed in order to design RS TPCs that are compatible with the performance requirements imposed by the two applications. Then, a novel ultrahigh-speed parallel architecture for turbo decoding of product codes is described. A comparison with binary Bose-Chaudhuri-Hocquenghem (BCH) TPCs is performed. The results show that high-rate RS TPCs offer a better complexity/performance tradeoff than BCH TPCs for low-cost Gbps fiber optic communications.

[1]  Robert G. Gallager,et al.  Low-density parity-check codes , 1962, IRE Trans. Inf. Theory.

[2]  O. Antoine,et al.  Theory of Error-correcting Codes , 2022 .

[3]  Govind P. Agrawal,et al.  Lightwave technology : telecommunication systems , 2005 .

[4]  Gabriella Bosco,et al.  Soft decoding in optical systems , 2003, IEEE Trans. Commun..

[5]  Ramesh Pyndiah,et al.  Some Results on the Binary Minimum Distance of Reed-Solomon Codes and Block Turbo Codes , 2007, 2007 IEEE International Conference on Communications.

[6]  Michel Joindot,et al.  Forward error correction in WDM PON using spectrum slicing , 2007, Opt. Switch. Netw..

[7]  Peter Sweeney,et al.  Iterative soft-decision decoding of linear block codes , 2000 .

[8]  Ludo M. G. M. Tolhuizen More results on the weight enumerator of product codes , 2002, IEEE Trans. Inf. Theory.

[9]  T. Mizuochi,et al.  Recent progress in forward error correction and its interplay with transmission impairments , 2006, IEEE Journal of Selected Topics in Quantum Electronics.

[10]  Ramesh Pyndiah,et al.  Block Turbo Code with Binary Input for Improving Quality of Service , 2002 .

[11]  ITU-T Rec. G.975.1 (02/2004) Forward error correction for high bit-rate DWDM submarine systems , 2005 .

[12]  Gabriella Bosco,et al.  Channel Coding for Optical Communications , 2005 .

[13]  Camille Leroux,et al.  Full-parallel architecture for turbo decoding of product codes , 2006 .

[14]  Ramesh Pyndiah,et al.  Performance of Reed-Solomon block turbo code , 1996, Proceedings of GLOBECOM'96. 1996 IEEE Global Telecommunications Conference.

[15]  Ken Gracie,et al.  Turbo and Turbo-Like Codes: Principles and Applications in Telecommunications , 2007, Proceedings of the IEEE.

[16]  Massinissa Lalam,et al.  An improved iterative decoding algorithm for block turbo codes , 2006, 2006 IEEE International Symposium on Information Theory.

[17]  Ramesh Pyndiah,et al.  Low-Complexity High-Rate Reed--Solomon Block Turbo Codes , 2007, IEEE Transactions on Communications.

[18]  W. W. Peterson,et al.  Encoding and error-correction procedures for the Bose-Chaudhuri codes , 1960, IRE Trans. Inf. Theory.

[19]  David Chase,et al.  Class of algorithms for decoding block codes with channel measurement information , 1972, IEEE Trans. Inf. Theory.

[20]  Christophe Jégo,et al.  Towards Gb/s turbo decoding of product code onto an FPGA device , 2007, 2007 IEEE International Symposium on Circuits and Systems.

[21]  I.B. Djordjevic,et al.  Low-density parity-check codes for 40-gb/s optical transmission systems , 2006, IEEE Journal of Selected Topics in Quantum Electronics.

[22]  Keshab K. Parhi,et al.  High speed VLSI architecture design for block turbo decoder , 2002, 2002 IEEE International Symposium on Circuits and Systems. Proceedings (Cat. No.02CH37353).

[23]  Roberto Garello,et al.  On the Weight Enumerator and the Maximum Likelihood Performance of Linear Product Codes , 2006, ArXiv.

[24]  N. Zierler,et al.  A Class of Error-Correcting Codes in $p^m $ Symbols , 1961 .

[25]  Takashi Mizuochi Recent Progress in Forward Error Correction for Optical Communication Systems , 2005, IEICE Trans. Commun..

[26]  Jing Li,et al.  On channel models for predicting soft-decision error correction performance in optically amplified systems , 2003, OFC 2003 Optical Fiber Communications Conference, 2003..

[27]  Bahram Honary,et al.  Fast Chase algorithm with an application in turbo decoding , 2001, IEEE Trans. Commun..

[28]  Daniel J. Costello,et al.  Channel coding: The road to channel capacity , 2006, Proceedings of the IEEE.

[29]  Ramesh Pyndiah,et al.  Near optimum decoding of product codes , 1994, 1994 IEEE GLOBECOM. Communications: The Global Bridge.

[30]  Aaas News,et al.  Book Reviews , 1893, Buffalo Medical and Surgical Journal.

[31]  K. Motoshima,et al.  Forward error correction based on block turbo code with 3-bit soft decision for 10-Gb/s optical communication systems , 2004, IEEE Journal of Selected Topics in Quantum Electronics.

[32]  A. Glavieux,et al.  Near Shannon limit error-correcting coding and decoding: Turbo-codes. 1 , 1993, Proceedings of ICC '93 - IEEE International Conference on Communications.

[33]  Ramesh Pyndiah,et al.  New architecture for high data rate turbo decoding of product codes , 2002, Global Telecommunications Conference, 2002. GLOBECOM '02. IEEE.

[34]  R. Blahut Algebraic Codes for Data Transmission , 2002 .

[35]  Duncan H. Lawrie,et al.  Access and Alignment of Data in an Array Processor , 1975, IEEE Transactions on Computers.